Originally Posted by
Silver
The solenoid is just a big relay - it has two little wires that go in and out, one positive, one negative. These pull in an electromagnetic switch that is connected to the big wires that carry the current that actually goes to the starter.
Knowing that, one can put the car in neutral, ignition on, and run a jumper lead from the positive terminal on the battery down to the big wire that goes from the solenoid to the starter - either at the solenoid or starter end, whichever is more accessible.
Another technique to deal with solenoids is to give them a lightish to medium tap with a hammer, as sometimes they just jam.